The crusader leader who refused the title King of Jerusalem and used the title Defender, or Advocate, of the Holy Sepulchre was Godfrey of Bouillon.
After Jerusalem was captured in July 1099, the crusaders needed a ruler for the new Latin state. Godfrey was selected after Raymond of Toulouse declined the crown. Godfrey accepted authority over the city but avoided the title king, traditionally explained by the belief that no earthly ruler should wear a golden crown where Jesus had worn a crown of thorns.
His Latin title was Advocatus Sancti Sepulchri, commonly translated as Advocate or Defender of the Holy Sepulchre. He ruled from 1099 until his death in 1100. During that brief period, he defended the new conquest against the Fatimid forces of Egypt and helped consolidate the crusaders’ position around Jerusalem.
Historians note that contemporary sources do not use his title consistently, so the exact terminology is debated. That scholarly qualification does not change the standard quiz answer: Godfrey of Bouillon was the first Latin ruler of Jerusalem and did not take the title King of Jerusalem.